GATE EC 2005


Question 1
The following differential equation has
3(\frac{d^{2}y}{dt^{2}})+4(\frac{dy}{dt})^{3}+y^{2}+2=x
A
degree = 2, order = 1
B
degree = 3, order = 2
C
degree = 4, order = 3
D
degree = 2, order = 3
Engineering Mathematics   Differential Equations
Question 1 Explanation: 
Order is highest derivative term. Degree is power of highest derivative term.
Question 2
Choose the function f (t); -\infty \lt t \lt \infty for which a Fourier series cannot be defined.
A
3sin(25t)
B
4cos(20t+3)+2sin(10t)
C
exp(-|t|)sin(25t)
D
1
Signals and Systems   Fourier Series
Question 2 Explanation: 
All other functions are either periodic or constant function.


Question 3
A fair dice is rolled twice. The probability that an odd number will follow an even number is
A
1/2
B
1/6
C
1/3
D
1/4
Engineering Mathematics   Probability and Statistics
Question 3 Explanation: 
\begin{aligned} P_{0}=\frac{3}{6}=\frac{1}{2} \\ P_{e}=\frac{3}{6}=\frac{1}{2} \end{aligned}
since both events are independent of each other.
P_{\text {(odd/even) }}=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}
Question 4
A solution of the following differential equation is given by \frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0
A
y=e^{2x}+e^{-3x}
B
y=e^{2x}+e^{3x}
C
y=e^{-2x}+e^{3x}
D
y=e^{-2x}+e^{-3x}
Engineering Mathematics   Differential Equations
Question 4 Explanation: 
\begin{aligned} A E \Rightarrow\quad D^{2}-5 D+6&=0 \\ (D-2)(D-3) &=0 \\ D &=2,3 \\ \therefore \quad y &=e^{2 x}+e^{3 x} \end{aligned}
Question 5
The function x(t) is shown in the figure. Even and odd parts of a unit step function u(t) are respectively,
A
\frac{1}{2},\frac{1}{2}x(t)
B
-\frac{1}{2},\frac{1}{2}x(t)
C
\frac{1}{2},-\frac{1}{2}x(t)
D
-\frac{1}{2},-\frac{1}{2}x(t)
Signals and Systems   Basics of Signals and Systems
Question 5 Explanation: 
\begin{array}{l} \text { Even part }=\frac{u(t)+u(-t)}{2}\\ \text { Odd part }=\frac{u(t)-u(-t)}{2} \end{array}








There are 5 questions to complete.